Pfaffian forms and \(\Delta\)-matroids with coefficients (Q1910553)

Let \(G\) be a connected graph with \(n\) vertices and \(m\) edges. If each edge is independently operational with probability \(p\) then the reliability of \(G\) is the probability that the operational edges form a spanning connected subgraph. This amount can be written as \[ p^{n- 1} \sum^{m- n+ 1}_{i= 0} H_i(1- p)^i \] and the (nonnegative integer) coefficients \(H_i\) form the \(H\)-vector.